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Contests
National and Regional Contests
Bulgaria Contests
IFYM Int. Fest. of Young Mathematicians, Sozopol
2010 IFYM, Sozopol
2
Function
Function
Source:
June 5, 2016
function
Problem Statement
Known
f
:
N
0
→
N
0
f:\mathbb{N}_0 \to \mathbb{N}_0
f
:
N
0
→
N
0
function for
∀
x
,
y
∈
N
0
\forall x,y\in \mathbb{N}_0
∀
x
,
y
∈
N
0
the following terms are paid
(
a
)
.
f
(
0
,
y
)
=
y
+
1
(a). f(0,y)=y+1
(
a
)
.
f
(
0
,
y
)
=
y
+
1
(
b
)
.
f
(
x
+
1
,
0
)
=
f
(
x
,
1
)
(b). f(x+1,0)=f(x,1)
(
b
)
.
f
(
x
+
1
,
0
)
=
f
(
x
,
1
)
(
c
)
.
f
(
x
+
1
,
y
+
1
)
=
f
(
x
,
f
(
x
+
1
,
y
)
)
.
(c). f(x+1,y+1)=f(x,f(x+1,y)).
(
c
)
.
f
(
x
+
1
,
y
+
1
)
=
f
(
x
,
f
(
x
+
1
,
y
))
.
Find the value if
f
(
4
,
1981
)
f(4,1981)
f
(
4
,
1981
)
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